Question: The grades on a math midterm at Springer are normally distributed with $\mu = 77$ and $\sigma = 4.5$. Christopher earned a $76$ on the exam. Find the z-score for Christopher's exam grade. Round to two decimal places.
Explanation: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Christopher's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{76 - {77}}{{4.5}}} $ ${ z \approx -0.22}$ The z-score is $-0.22$. In other words, Christopher's score was $0.22$ standard deviations below the mean.